Selective sampling with Gromov–Hausdorff metric:Efficient dense-shape correspondence via Confidence-based sample consensus

Background Functional mapping, despite its proven efficiency, suffers from a “chicken or egg” scenario, in that, poor spatial features lead to inadequate spectral alignment and vice versa during training, often resulting in slow convergence, high computational costs, and learning failures, particularly when small datasets are used. Methods A novel method is presented for dense-shape correspondence, whereby the spatial information transformed by neural networks is combined with the projections onto spectral maps to overcome the “chicken or egg” challenge by selectively sampling only points with high confidence in their alignment. These points then contribute to the alignment and spectral loss terms, boosting training, and accelerating convergence by a factor of five. To ensure full unsupervised learning, the Gromov–Hausdorff distance metric was used to select the points with the maximal alignment score displaying most confidence. Results The effectiveness of the proposed approach was demonstrated on several benchmark datasets, whereby results were reported as superior to those of spectral and spatial-based methods. Conclusions The proposed method provides a promising new approach to dense-shape correspondence, addressing the key challenges in the field and offering significant advantages over the current methods, including faster convergence, improved accuracy, and reduced computational costs.

The Deconvolution Method for Obtaining Correspondence in Data-Independent Acquisition Mass Spectrometry Data

Although data-independent acquisition (DIA) shows powerful potential in achieving comprehensive peptide information acquisition, the difficulty in determining the precursor m/z and distinguishing fragment ions has posed challenges in DIA data analysis. To address this challenge, a common approach is to recover the correspondence between precursor ions and fragment ions, followed by peptide identification using traditional data-dependent acquisition (DDA) database searching. In this study, we propose a cosine similarity-based deconvolution method that rapidly establishes the correspondence between chromatographic profiles of precursor ions and fragment ions through matrix calculations. Experimental results demonstrate that our method, referred to as CosDIA, yields a peptide identification count close to that of DIA-umpire. However, compared to DIA-umpire, we can establish the correspondence between original MS/MS spectra and pseudo-MS/MS spectra. Furthermore, compared to the CorrDIA method, our approach achieves higher efficiency in terms of time, reducing the time cost of the analysis process. These results highlight the potential advantages of the CosDIA method in DIA data analysis, providing a powerful tool and method for large-scale proteomics research.

Solving Algebraic Problems with Geometry Diagrams Using Syntax-Semantics Diagram Understanding

Solving Algebraic Problems with Geometry Diagrams(APGDs)poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects.Problems typically involve both textual descriptions and geometry diagrams,requiring a joint understanding of these modalities.Although considerable progress has been made in solving math word problems,research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs,which limits their ability to effectively solve problems.In this study,a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information.The three-phase scheme begins with the application of the statetransformer paradigm,modeling the problem-solving process and effectively representing the intermediate states and transformations during the process.Next,a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams.Finally,a specific algorithm is designed focusing on diagram understanding,which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram.A method for generating derived relations,which are essential for solving APGDs,is also introduced.Experiments on real-world datasets,including geometry calculation problems and shaded area problems,demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.

Application of Lexical Approach to Teaching of Business English Correspondence

Because of poor vocabulary, improper use of lexis, and interference of first language, it is difficult for students in voca-tional school to learn Business English Correspondence well. Business English has close relations with lexical chunks, whichmakes it necessary to apply lexical approach to teaching of Business English Correspondence. This paper intends to explore its the-oretical foundations and emphasize how to apply lexical approach to teaching of Business English Correspondence in vocationalschool.

不依赖于连续性假设的Correspondence Manifold研究

图像匹配是计算机视觉中的一个基本问题,现有方法一般基于极几何模型,在使用中往往存在效率不高和对有些错误匹配点无法剔除的问题,为此研究了图像匹配中的模型问题.首先通过分析图像对应点映射关系的特点及其在联合图像空间中所形成曲面的几何直观,给出了不依赖于连续性假设的对应流形(CM)定义;然后通过分析CM及其视图所体现的映射关系特点和完备性,直观地给出了基于对应函数的CM表征方案,据此将CM的学习归结为一般的函数回归问题;最后通过理论分析和实验方式探讨了CM模型相比于经典的极几何模型的优势.理论分析结果表明,CM模型在图像匹配关系的描述中给出的是充分必要约束,而极几何模型给出的是必要非充分约束;实际图像匹配的实验结果表明,基于CM的错误匹配剔除方法的准确性和稳健性比基于极几何模型的方法略好,且候选匹配中错误越多,CM的速度优势越明显.

Pragmatic Vagueness in Business Correspondences——A Perspective of PP

Pragmatic vagueness is frequently used in business correspondences and it offers benefits to the addressers by making business letter more flexible,appropriate and polite.This paper focuses on the employment of vague language in international business correspondences based on the Politeness Principle.In this study,the pragmatic effect of vague language in business correspondence is illustrated and summarized as a motivated factor to better show politeness and respect.The use of vague language motivated by politeness consequently leads to a more smooth,successful and desired communication in business world.

Analysis of Vague Language in Enquiry and Offers——from English business correspondence

English business correspondence plays an important role in business activities. People take it for granted that it should be cautious and accurate,but neglect the necessity and importance of vague language. Therefore, it is very important to apply vague language to English business correspondence.

Correct Expression of Post-positive Attributives in Foreign Trade English Correspondence

The Foreign Trade English Correspondence is one of the main courses of International Trade majors.Due to the habit of thinking in Chinese,students usually cannot correctly and flexibly use post-positive attributives in the correspondence writing of foreign trade.Participle phrases,prepositional phrases,attributive clauses,infinitive phrases,adjective phrases and apposition clauses all can follow nouns as post-positive attributives to modify nouns.Mastering the correct expression of post-positive attrib⁃utives will help students improve their writing competence of foreign trade correspondence.

Study on the Characteristics of Urban Air Pollution Based on Correspondence Analysis--A Case Study of Six Provincial Capitals in Central-south China

[Objective] The aim was to study the characteristics of urban air pollution on the basis of correspondence analysis.[Method] By using the correlated data from China Statistical Yearbook in 2010,a correspondence analysis on the air pollution indicators(like respirable particles,SO2 and NO2) of six provincial capitals in central-south China was carried out by means of SPSS software,and the characteristics of air pollution in the cities of China during different industrialization stages were summarized further.[Result] In the cities during early industrialization(like Nanning City and Guiyang City) and mineral resource-based cities(like Taiyuan City),the air was mainly polluted by SO2;for the cities in the middle industrialization(such as Changsha City,Wuhan City,Zhengzhou City and Chengdu City),the air was polluted by respirable particles chiefly;in the cities in late industrialization(like Guangzhou City and Shenzhen City) or completing industrialization(like Shanghai City),the air was mainly polluted by NO2;for the cities in pre-industrial stage(like Haikou City and Lhasa City),the characteristic of air pollution wasn’t obvious.[Conclusion] The study could provide references for the control of urban air pollution in China in the further.

Improved method for zero-energy mode suppression in peridynamic correspondence model

The peridynamic correspondence model provides a general formulation to incorporate the classical local model and,therefore,helps to solve mechanical problems with discontinuities easily.But it suffers from zero-energy mode instability in numerical implementation due to the approximation of deformation gradient tensor.To suppress zero-energy modes,previous stabilized methods were generally more based on adding a supplemental force state derived from bond-based peridynamic theory,which requires a bond-based peridynamic micro-modulus.In this work,we present an improved stabilized method where the stabilization force state is derived directly from the peridynamic correspondence model.Hence,the bond-based peridynamic micro-modulus is abandoned.This improved method needs no extra constant to control the magnitude of stabilization force state and it is suitable for either isotropic or anisotropic materials.Several examples are presented to demonstrate its performance in simulating crack propagation,and numerical results show its efficiency and effectiveness.

Behavior Consistency Computation for Workflow Nets With Unknown Correspondence

Consistency degree calculation is established on the basis of known correspondence, but in real life, the correspondence is generally unknown, so how to calculate consistency of two models under unknown correspondence has become a problem. For this condition, we should analyze unknown correspondence due to the influence of different correspondences.In this paper we obtain the relations of transitions based on event relations using branching processes, and build a behavioral matrix of relations. Based on the permutation of behavioral matrix, we express different correspondences, and define a new formula to compute the maximal consistency degree of two workflow nets. Additionally, this paper utilizes an example to show these definitions, computation as well as the advantages.

EQUILIBIA OF NONCOMPACT GENERALIZED GAMES WITH CORRESPONDENCES WITHOUT OPEN LOWER SECTIONS

The new classes of Fc-correspondences and Fc -majorised correspondenceswithout open lower sections is introduced. Some existence theorems of madximal elements ofthe Fc -correspondences and the Fc-majorized correspondences defined on noncompactset in topological vector spaces are obtained. As applications, some existence theoremsof equilibrium points for one-person games, qualitative games and generalized games withthe Fc -majorized correspondences devined on noncompact strategy sets in topologicalvector spaces are also given. These theorems improve and generalize several known resultsin recent literature.

Weakly δ-continuous Correspondences on Super-space

In the paper,we define weakly δ-continuous correspondences on super-space,On the basis of δ-open(closed) sets,θ-open(closed) sets and regular open(closed) sets in topological space,some equivalent conditions of this kind of correspondences are obtained,and some applications of subset nets and convergence nets are given.

A Simple Mathematical Formulation of the Correspondence Principle

In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr’s correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume that the Fourier coefficients coincide for the case of large quantum number. We illustrate the procedure by analyzing the classical limit for the quantum harmonic oscillator and the particle in a box, although the method is quite general. We find, in an analytical fashion, the classical distribution arising from the quantum one as the zeroth order term in an expansion in powers of Planck’s constant. We interpret the correction terms as residual quantum effects at the microscopic-macroscopic boundary.

State-Dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in Non-Hermitian Topological Systems with Generalized Inversion Symmetry

Breakdown of bulk-boundary correspondence in non-Hermitian(NH)topological systems with generalized inversion symmetries is a controversial issue.The non-Bloch topological invariants determine the existence of edge states,but fail to describe the number and distribution of defective edge states in non-Hermitian topological systems.The state-dependent topological invariants,instead of a global topological invariant,are developed to accurately characterize the bulk-boundary correspondence of the NH systems,which is very different from their Hermitian counterparts.At the same time,we obtain the accurate phase diagram of the one-dimensional non-Hermitian Su–Schrieffer–Heeger model with a generalized inversion symmetry from the state-dependent topological invariants.Therefore,these results will be helpful for understanding the exotic topological properties of various non-Hermitian systems.

CORRESPONDENCE ANALYSIS ON IMAGES OF JIANGXI PROVINCE AS A TOURIST DESTINATION

This paper delineates the images of Jiangxi Province as tourist destination perceived by about 2000 sample visitors at Lushan Mountain and other 3 famous resorts (Jinggangshan Mountains, Longhushan Mountain, and Sanqingshan Mountain), with a result that the most common image is the famous scenic mountain image with partial attribute of image of religious culture destination. In order to reveal the similarities and dissimilarities of images among the four destinations, a correspondence analysis on 16 image attributes was employed. The results indicate that the tourists’ images on Longhushan Mountain, Sanqingshan Mountain and Lushan Mountain are very similar: having a lot of good tourist sites, famous mountain scenery, being close to nature and having good guide service, and others, but religious culture and good shopping facilities having not made deep impression on tourist, while Jinggangshan Mountains is famous for its red culture. The correspondence analysis visualizes the strengths and weaknesses of the destinations, which is useful for market positioning among the competitive places. Finally, some marketing suggestions for the four destinations were provided.

A New Method for Pose Estimation from Line Correspondences

我们能通常在一个一般位置从三根线决定目标的姿势。三的配置非 -- 在二个点交叉的共面的线有一些特别特征，在一个一般位置的三根线没有它。这里，我们在场用这种特别的线配置决定目标姿势的一个新方法。在理论，这个方法从三线通讯充实姿势评价方法。另外，它为实际应用提供指导。而且，我们建议一个方法处理多答案现象和一个新反复的方法。模拟结果证明我们的算法快速地并且要用体力地工作。

On the Effects of Negative Transfer of Native Language to Business English Correspondence from the Analysis on the Errors Madein Clarity

This paper is an attempt to analyse the role of negative transfer in the acquisition of business English correspondence through the analysis of errors made in learners’writings.The analysis is focused on errors made violating clarity.Through the contrast between those errors and the normative samples,one of the deep-rooted reasons that prohibits learners to make the correspondences be clarified are discovered,which is the negative transfer resulted from different thought patterns affected by the cultural diversities.

Correspondence normalized ghost imaging on compressive sensing

Ghost imaging （GI） offers great potential with respect to conventional imaging techniques. It is an open problem in GI systems that a long acquisition time is be required for reconstructing images with good visibility and signal-to-noise ratios （SNRs）. In this paper, we propose a new scheme to get good performance with a shorter construction time. We call it correspondence normalized ghost imaging based on compressive sensing （CCNGI）. In the scheme, we enhance the signal-to-noise performance by normalizing the reference beam intensity to eliminate the noise caused by laser power fluctuations, and reduce the reconstruction time by using both compressive sensing （CS） and time-correspondence imaging （CI） techniques. It is shown that the qualities of the images have been improved and the reconstruction time has been reduced using CCNGI scheme. For the two-grayscale ＂double-slit＂ image, the mean square error （MSE） by GI and the normalized GI （NGI） schemes with the measurement number of 5000 are 0.237 and 0.164, respectively, and that is 0.021 by CCNGI scheme with 2500 measurements. For the eight-grayscale ＂lena＂ object, the peak signal-to-noise rates （PSNRs） are 10.506 and 13.098, respectively using G1 and NGI schemes while the value turns to 16.198 using CCNGI scheme. The results also show that a high-fidelity GI reconstruction has been achieved using only 44% of the number of measurements corresponding to the Nyquist limit for the two-grayscale ＂double-slit＂ object. The qualities of the reconstructed images using CCNGI are almost the same as those from GI via sparsity constraints （GISC） with a shorter reconstruction time.

Rejecting Outliers Based on Correspondence Manifold

发现在二幅图象之间的可靠的相应的点是在计算机视觉的一个基本问题，特别与 L 视觉框架的发展。这篇论文介绍歧管的通讯并且建议一个新奇计划由听说向上的看法拒绝孤立点歧管。建议计划独立于在出版工作要估计并且克服可得到的方法的下列限制的参量的模型：效率严厉地因孤立点百分比的增加和估计的模型参数的数字倒下；孤立点拒绝被结合模型选择和模型评价。真实图象对的实验显示出我们的建议计划的优秀性能。